In digital imaging systems, color management is the controlled conversion between the color representations of various devices, such as image scanners, digital cameras, monitors, TV screens, film printers, computer printers, offset presses, and corresponding media. One goal of color management is to obtain a good match across color devices; for example, a video which should appear the same color on a computer LCD monitor, a plasma TV screen, and on a printed frame of video. Color management helps to achieve the same appearance on all of these devices, provided the devices are capable of delivering the needed color intensities. Color imaging technology has become almost ubiquitous in modern life. For a more comprehensive introduction into the many facets of color imaging, see: Digital Color Imaging Handbook, by: Gaurav Sharma (Ed.), CRC Press (December 2002), ISBN-13: 978-0-8493-09007, which is incorporated herein in its entirety by reference.
One key issue in color imaging is how to deal with a color that cannot be reproduced on a certain device in order to show it through a different device as if it were visually the same color, just as when the reproducible color range between color transparencies and printed matters are different. There is no common method for this process, and the performance depends on the capability of each color matching method. Digital halftoning is a process in which digital input signals to a binary digital printer are modified prior to outputting an image such that the printed image creates the illusion of the continuous tone (contone) of the original color image. Much effort in the field of digital halftoning is directed to developing sophisticated algorithms used to best match specific color parameters of an output device to input colors such that the source image is accurately reproduced on the output device. For a more comprehensive introduction to halftones, see: Chapter 6—Digital Color Halftones, in the above-referenced Digital Color Imaging Handbook. 
One halftone method is referred to as screening. Halftone screening compares requested contone levels to predetermined threshold levels typically defined over a rectangular cell that is tiled to fill the image plane. If the contone level at a spot is greater than the threshold level, a spot is printed; otherwise, a spot is not printed. The output of the screening process is a binary pattern of multiple small dots which are regularly spaced as determined by the addressability of the imaging system. Marking processes such as electro-photography and offset printing typically cluster the small dots within a cell because a large clustered mass prints with more consistent size and density than small spots printed with individual isolated pixels. The alignment of the clusters via the halftone-cell tiling defines the geometry of the halftone screen. The resulting halftone structure is a two-dimensionally repeated pattern, possessing two fundamental spatial frequencies determined by the geometry of the halftone screen.
A cluster based halftone screen contains only a single center or multiple centers which have similar geometries. For many digital halftone printers, the use of single-center halftone screens is limited because of the relatively fewer number of levels. A single cell usually does not contain a large number of pixels. Therefore, it cannot provide enough simulated contone levels as desired by many sophisticated color reproduction tasks. A common approach to overcome this problem is employing halftone screens with multiple centers (M), such as dual-dots (M=2), quad-dots (M=4), and stoclustic screens (M as large as a few hundred).
One important performance measure of a printing device is the tone reproduction curve, often referred to as the TRC. The TRC defines the color output given a specified color input. The tone reproduction curve can be determined by measurement using, for example, a calorimeter. For all possible binary patterns produced by a halftone process with a halftone screen and spatially constant inputs, the outputs of printed test patches are measured and the color differences between the printed patches and the paper can be calculated from the measurements and plotted against the input levels as the desired TRC. For devices with single-cell cluster screens, it is a practical approach to obtain the complete TRCs since the number of measurements required to be obtained is relatively small. Since multi-center cluster screens provide many more distinguishable levels to enable high-quality color output, such an approach becomes no longer practical to accurately measure the raw data necessary to generate the TRC for device's with multi-center halftone screens. Unlike for single-center screens, it can be difficult and time consuming to print and measure hundreds (or perhaps thousands) of halftone patterns for all possible input levels. Usually this problem is solved by empirical approaches using sampled measurements and mathematic functions to determining the TRCs. One such approach for algorithmically determining TRCs is based on the Yule-Nielsen modified spectral Neugebauer model (YNN). For a more thorough discussion of the YNN model, see: Principles of Color Reproduction, by: John Yule, Gary Field, Graphic Arts Technical Foundation Press, 2nd Rev. Ed. (2001), ISBN-13: 978-0-8836-22223.
For a given halftone pattern containing a single colorant, the YNN model is given by:R1/γ(λ)=(1−a)Rp1/γ(λ)+aRc1/γ(λ)  (1)
where R(λ) is the estimated average spectral reflectance of the halftone pattern at wavelength (λ), a is the fractional area covered by the toner or ink, and Rp(λ) and Rc(λ) are the measured spectral reflectances of the paper (a=0%) and solid toner (a=100%), respectively. The fitting parameter γ depends on the amount of light diffusion in the paper and typically is between a value of 1 and 10. Once the reflectance spectra of the paper and the solid toner have been measured, the reflectance spectrum of the halftone pattern can be calculated with an estimated toner coverage of the fractional coverage area. The coverage area can be determined directly from the digital binary halftone pattern. The YNN model has been shown to provide reasonable predictions. Model-based approaches tend to be more efficient. However, the accuracy of a model's prediction can be limited due to the difficulty of estimating the true toner coverage of a particular halftone pattern because the actual outputs from different printers can be complicated and because adjacent printed pixels tend to overlap. Further, physical halftone outputs have irregular shapes and their size, shape and density can vary with time and location. The scattering of light in the paper substrate adds further complexity thereby making a detailed microscopic model of the dot overlapping difficult to construct. Even with a well defined digital binary description, the true area covered by toner of a halftone pattern can be difficult to accurately measure. Another drawback is that such model-based methods tend to yield relatively large errors in the derived TRCs. Such errors may cause artifacts to arise in the color outputs of devices which have been characterized using such derived TRCs.
Accordingly, what is needed in this art is a new method for tone reproduction curve estimation for devices equipped with multi-center cluster halftone screens which combines the accuracy of measurement-based approaches with the efficiency of model-based approaches.